Vladimir Kramnik, former world chess champion and current No. 4, is playing in the first round of the London Chess Classic, the most competitive chess tournament to be played in the U.K. capital in 25 years. Tall, handsome and expressionless, he looks exactly as a man who has mastered a game of nearly infinite variation should: like a high-end assassin. Today, however, he is getting methodically and mercilessly crushed.

His opponent is a teenager who seems to be having difficulty staying awake. Magnus Carlsen yawns, fidgets, slumps in his chair. He gets up and wanders over to the other games, staring at the boards like a curious toddler. Every now and then, he returns to his own game and moves one of his pieces, inexorably building an attack so fierce that by the 43rd move Kramnik sees the hopelessness of his position and resigns. (See the top sports stories of 2009.)

Genius can appear anywhere, but the origins of Carlsen's talent are particularly mysterious. In November, Carlsen, then 18, became the youngest world No. 1 in the game's history. He hails from Norway  a "small, poxy chess nation with almost no history of success," as the English grand master Nigel Short sniffily describes it  and unlike many chess prodigies who are full-time players by age 12, Carlsen stayed in school until last year. His father Henrik, a soft-spoken engineer, says he has spent more time urging his young son to complete his schoolwork than to play chess. Even now, Henrik will interrupt Carlsen's chess studies to drag him out for a family hike or museum trip. "I still have to pinch my arm," Henrik says. "This certainly is not what we had in mind for Magnus."

Even pro chess players  a population inured to demonstrations of extraordinary intellect  have been electrified by Carlsen's rise. A grand master at 13 (the third youngest in history) and a conqueror of top players at 15, he is often referred to as the Mozart of chess for the seeming ease of his mastery. In September, he announced a coaching contract with Garry Kasparov, arguably the greatest player of all time, who quit chess in 2005 to pursue a political career in Russia. "Before he is done," Kasparov says, "Carlsen will have changed our ancient game considerably." (See pictures of the late chess prodigy Bobby Fischer.)

In conversation, Carlsen offers only subtle clues to his intelligence. His speech, like his chess, is technical, grammatically flawless and logically irresistible. He dresses neatly but shows a teenager's discomfort with formality. (He rarely makes it through a game without his shirt coming untucked.) He would seem older than 19 but for his habit of giggling and his coltlike aversion to eye contact.

Carlsen joins chess's élite at a time of unprecedented change. He is one of a generation of players who learned the game from computers. To this day, he's not certain if he has an actual board at home. "I might have one somewhere. I'm not sure," he says. Powerful chess programs, which now routinely beat the best human competitors, have allowed grand masters to study positions at a deeper level than was possible before. Short says top players can now spend almost an entire game trading moves that have been scripted by the same program and that such play by rote has removed some of the mystique of chess. He likens chess computers to "chainsaws chopping down the Amazon." (Read a Q&A with Carlsen.)

But Kasparov says Carlsen's mastery is rooted in a "deep intuitive sense no computer can teach" and that his pupil "has a natural feel for where to place the pieces." According to Kasparov, Carlsen has a knack for sensing the potential energy in each move, even if its ultimate effect is too far away for anyone  even a computer  to calculate. In the grand-master commentary room, where chess's clerisy gather to analyze play, the experts did not even consider several of Carlsen's moves during his game with Kramnik until they saw them and realized they were perfect. "It's hard to explain," Carlsen says. "Sometimes a move just feels right."

Not that Carlsen lacks computational prowess, though. He often calculates 20 moves ahead and can comfortably play several games simultaneously while blindfolded simply by hearing each move in notation. The fear surrounding any such beautiful mind is that a life spent probing the edges of the infinite  the possible permutations of a chess game outnumber the estimated number of atoms in the universe  will eventually lead to madness. Grand masters say Carlsen's precociousness is reminiscent of Bobby Fischer's. The great American player spent his later years in isolation, reappearing only to spout anti-Semitic conspiracy theories. "It's easy to get obsessed with chess," Carlsen says. "That's what happened with Fischer and Paul Morphy," another prodigy lost to madness. "I don't have that same obsession." (Read: "Fischer vs. Spassky: Battle of the Brains.")

Although firmly atop the chess rankings, thanks in part to his victory in London, Carlsen must now fight his way through a series of qualifying competitions in order to earn a chance to play for the world-championship title  the game's highest prize, which is contested every two or three years. His father says he is more concerned about "whether chess will make him a happy person." It seems to be doing just that. "I love the game. I love to compete," Carlsen says. Asked how long he will continue to enjoy chess and where the game will take him, Carlsen pauses to ponder the variables. "It's too difficult to predict," he concludes. So far, at least, he's been making all the right moves.